To determine the molar mass of the polymer, we can use the equation for osmotic pressure:
π = MRT
Where:
π = osmotic pressure in atm
M = molar mass of the solute in g/mol
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature in Kelvin
First, let's convert the given osmotic pressure to atm:
1 Torr = 1/760 atm
So, 0.808 Torr = 0.808/760 atm = 0.00106316 atm
Next, convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 21°C + 273.15 = 294.15 K
Now, we rearrange the equation to solve for the molar mass of the polymer:
M = πRT / P
Substituting the given values:
M = (0.00106316 atm) * (0.0821 L·atm/(mol·K)) * (294.15 K) / (0.17 g) = 14165.68 g/mol
Therefore, the molar mass of the polymer is approximately 14165.68 g/mol.